Cats are obligate carnivores but they can have plant foods. Most of their diet should be meat. Some cats like to snack on grasses like wheat or barley. My cat stays indoors; but if your cat eats a bird or mouse, your cat's prey may have undigested plant foods in its system.
And my cat can be finicky too, but she likes the flaxseed oil. She gets canned food for dinner, so I just mix it in.